Stochastic-SplitGAS: A Quantum Monte Carlo Multi-Reference Perturbation Theory Based on the Imaginary-Time Evolution of Effective Hamiltonians

Accurately modeling the electronic structure of systems with many unpaired electrons remains a major challenge in quantum chemistry. Qualitatively correct electronic structures generally require large active space multireference wave functions, while dynamic correlation effects beyond the active space are crucial for quantitatively accurate descriptions of magnetic, catalytic and optical properties of such systems. Here, we present an uncontracted multireference perturbation theory based on the FCIQMC imaginary-time evolution of effective Hamiltonians, built upon the generalized active space concept and Löwdin's partitioning technique. The configurational interaction space is split into a reference space, consisting of the most important configurations, and a perturber space, containing the more numerous configurations responsible for dynamic correlation effects. The generalized active space algorithm allows the flexible partitioning of the configurational space. Löwdin's partitioning technique is then used to construct an effective Hamiltonian which is stochastically solved. This strategy allows us to apply perturbative corrections on large active space reference wave functions, without requiring high-order reduced density matrices, which have been found the bottleneck in other perturbation theory strategies. The capabilities of the resulting method, called Stochastic-SplitGAS, are demonstrated on the triplet-quintet spin gap of an Fe(II)-porphyrin model system and the spin ladder of a [Fe(III)₂S₂]^2- complex.